President Obama is threatening to veto any legislation that extends all the tax cuts set to expire at the end of the year, as he presses Congress to extend those cuts only for families whose yearly income is less than $250,000 -- and raises taxes on everyone earning more.

The veto threat sets the early tone for what is expected to be a contentious battle between Democrats and Republicans through the rest of the year as they seek to avoid the so-called "taxmageddon" -- the sudden increase in taxes on all Americans that will occur if Congress doesn't vote to extend some or all of the Bush-era tax rates.

Obama will press his case Tuesday afternoon during an address at a community college in Iowa. Ahead of that speech, Republican National Committee Chairman Reince Priebus told Fox News that the president's proposal is a "sham" which, if enacted, would cut into already meager economic growth. He accused Obama of playing a "divisive rich versus poor game."

The president, amid such charges of class warfare, urged Congress Monday to pass a bill that deals with the middle-class tax rates only. Lawmakers then can move on to a separate debate over extending the rates for top earners, Obama said, though he made clear he is adamantly opposed to doing so.

"I will fight to end them," Obama said Monday, speaking in the East Room of the White House. He added that he doesn't want that debate to "threaten" those making less than $250,000.

When asked later in a TV interview with North Carolina's WRAL whether he would veto any bill that extended all the tax cuts, Obama said, "yes, and the reason is, we can't afford it."

In his earlier remarks at the White House, Obama argued that sustaining the current tax rates for top earners puts too big a hole in the federal budget, saying "we can't afford to keep that up." Obama called on Congress to extend those rates, for one year, for families earning less than $250,000 -- failure to do so, he said, would be a "blow" to families and a "drag" on the economy.

The proposal pre-empts a more sweeping proposal from congressional Republicans -- who will be negotiating for an extension of the Bush tax rates for everyone.

Senate Republican Leader Mitch McConnell's office panned the president's plan as a "call for tax hikes on small businesses."

The office noted that Obama said two years ago that letting the rates go up would be bad for the economy. On "CNN's State of the Union" Sunday, McConnell noted, "We have a slower growth rate today than we had then."

House Speaker John Boehner offered a similar rebuke, accusing Obama of "doubling down on his quixotic call for the same small businesses tax hikes that have been routinely rejected by the House and Senate."

Mitt Romney's campaign also pounced. "President Obama's response to even more bad economic news is a massive tax increase. It just proves again that the president doesn't have a clue how to get America working again and help the middle class," spokeswoman Andrea Saul said in a statement.

The proposal comes just days after Obama courted the blue-collar vote in the battleground states of Ohio and Pennsylvania, where he talked frequently about middle-class values.

The pitch is the latest proposal from a White House that has had a complicated relationship with the Bush-era tax rates, which have been in effect for nearly a decade. Obama at first held back on letting any of those rates expire during the height of the recession, saying in 2009 that would be "the last thing you want to do" because it would "take more demand out of the economy."

He then negotiated with Republicans in 2010 to extend the rates for another two years.

But campaign adviser Robert Gibbs said over the weekend that Obama is now "100 percent committed" to ending the rates for those making more than $250,000.

Obama's re-election campaign plans to use Washington's tax debate to ramp up its criticism of Romney. The campaign and its Democratic allies have slammed the presumptive GOP nominee for not releasing several years of tax returns and for having some of his money in offshore bank accounts.

The strategy is aimed at portraying Romney, whose personal wealth could exceed $250 million, as disconnected from middle-class voters.

"We have to continue to grow our economy. We have to grow it from the middle class out," Gibbs said Monday in an interview on NBC's "Today" show. "But for millionaires and billionaires, they don't need a tax cut," he added.

Obama is expected to promote his tax policy at a series of events this week in battleground states, including New Hampshire, Colorado and Nevada.

The Bush-era tax cuts are due to expire at the end of the year unless Congress votes to extend them. Economists worry that across-the-board tax increases, along with automatic spending cuts also scheduled to take hold at year's end, could be a blow to the shaky U.S. economy.

Fox News' Ed Henry and The Associated Press contributed to this report